Forward and Backward simulations of a power propulsion system L. Horrein (1) , A. Bouscayrol (1) , P. Delarue (1) , J. N. Verhille (2) , C. Mayet (1) (2) (1) L2EP, Université Lille1, France, Alain.Bouscayrol@univ-lille1.fr (2) Siemens, rue nationale, 59 000 Lille Abstract: This paper aims to compare a forward and backward simulation of the power propulsion system of an automatic subway. In the forward approach the control of the system is required. In the backward approach, no control is required but a derivative relationship has to be computed. Both simulations are compared in terms of accuracy of dynamical performances, maximal values of different variables and energy consumption and specifically when limitations occur. Keywords: traction systems, forward simulation, backward simulation, 1. INTRODUCTION Simulation is a key issue in the development of new transportation systems (Eshani et al, 2005) (Gao et al., 2007) (Chan et al., 2010). Indeed, energy consumption of transports is a challenge for the next decades (Rufer et al. 2004) (Chan, 2007) (Barrero et al., 2008). Even though, electric trains, tramways or subways have a high efficiency in comparison with other vehicles, new concepts are developed for the reduction of their consumption of energy (Foiadelli et al., 2006) (Destraz et al. 2007) (Steiner et al., 2007) (Ruelland et al. 2007). Different modelling and simulation approaches are used in function of different objectives (Guzella et al. 1999) (Trigui et al. 2004) (Chen et al. 2009), in classical softwares (Onoda et al 2004) (Amrheim et al., 2005), or for the development of dedicated softwares (Wipke et al. 1999) (Dempsey, 2006), In the forward approach, the simulation is realized from the cause (manipulation of energy) to the effect (velocity of the vehicle) with respect to the physical power flows in the system. A causal description is thus required: the integral causality yields a physical delay between inputs and outputs, as in the real system (Iwasaki et al, 1994) (Hautier et al, 2004). But, in order to get the desired velocity, a control must be defined. Indeed, the control loop will defined the energy needed to move the vehicle with the desired velocity. The drawback of such a method is thus that a control has to be designed. The advantage of a forward simulation is that any velocity can be achieved without prior knowledge of its evolution, as in the real life (Chan et al., 2010). Generally, a forward approach is more dedicated to define and tune the control of a system. In the case of the control, dynamical models are used and for study the energy consumption, we used statics models. Energetic Macroscopic Representation (EMR) (Bouscayrol et al. 2000) (Delarue et al., 2003) is a graphical description based on a forward integral causality for the development of control schemes. EMR has been successfully applied to HEVs (Chen et al, 2004) and innovative subways (Verhille et al, 2004) (Allègre et al., 2010). In the backward approach, the simulation is realized from the objective (drive cycle) to the cause (required energy) (Trigui et al., 2004). It is a way to anticipate to the energy needed to move the vehicle. Most of the time, static models are used because theirs inputs and outputs can be changed in any direction. Moreover the main dynamics of the system is considered and a differential equation is computed using a derivative causality. The advantage of a backward approach is that no control is required. The drawback of such a method is that the drive cycle must be known in advance because the derivation of velocity. Generally, a backward approach is used to have an overview of energy consumption and for component design. Many structural softwares use a backward approach such as PSAT (Milano, 2007), ADVISOR (Wipke et al., 1999), Dynmola (Dempsey, 2006), etc. The objective of this paper is to investigate the difference between a forward and backward simulation of the propulsion system of an automatic subway and specifically when limitations occur. In a previous paper (Horrein et al., 2011), the difference between dynamic, quasi-static and static models have been studied in terms of computation time and accuracy of energy consumption. In this paper, only a static model of the electric drive is considered. Forward and backward simulations are thus compared in terms of computation time, accuracy of dynamical performances, maximal values and energy consumption. The case of control limitations is specifically studied because most industrial applications have active limitations. 2. STUDIED TRACTION SYSTEM Subway VAL 208 is composed of two cars driven by 8 Permanent Magnet Synchronous Machines (PMSM), supplied by Voltages Source Inverters (VSI). Each machine is connected to a wheel through a gearbox (Fig. 1). A complete dynamical model has been developed for simulation. The initial dynamical model has been validated